Theory of heat dissipation in molecular electronics

In this paper we discuss various aspects of energy dissipation and heating of molecular junctions under bias. First-principles calculations based on density functional and nonequilibrium Green's functions are used to compute the power emitted in a molecule due to scattering with localized vibrations. In this context, we present a perturbation scheme in the electron-phonon coupling, that is found numerically reliable for the computation of the emitted power, because intrinsically it is current conserving. The balance between the rate of phonons emitted and dissipated into the contacts allows the computation of the steady-state distribution of phonon quanta localized in the junction, from which we extract the local temperature reached by the molecule. The model includes a microscopic approach for the computation of the phonon decay rate, accounting for the dynamical coupling between the vibrational modes localized on the molecule and the contact phonons. The method is applied to the discussion of several limiting conditions and trends, depending on electron-phonon coupling, incoherent transmission and phonon dissipation rate using both analytical results and numerical calculations.